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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Statistical analysis of data from single molecule experiment

Tomasz Burzykowski, Jacek Piotr Szubiakowski, Tobias Rydèn

Published Nov 18, 2003• 4 citations
Publisher

Abstract

The maximum-likelihood estimation method is considered. It is based on three-level Dehmelt scheme of isolated quantum system and it makes use of the theory of Markov-modulated Poison process. This method is applied to the analysis of the photon-counting distribution resulting from a single molecule fluorescence experiment. It is assumed that the data available for the estimation contain only the number of collected photons per time interval.

DOI
10.1117/12.544568

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The maximum-likelihood estimation method is considered. It is based on three-level Dehmelt scheme of isolated quantum system and it makes use of the theory of Markov-modulated Poison process. This method is applied to the analysis of the photon-counting distribution resulting from a single molecule fluorescence experiment. It is assumed that the data available for the estimation contain only the number of collected photons per time interval.
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We present a method for determining the atom number distribution of few atoms in a tight optical tweezer from their fluorescence distributions. In the tight tweezer regime, the detection light causes rapid atom loss due to light-assisted collisions. This in turn leads to non-Poissonian and overlapping fluorescence distributions for different initial atom numbers, and commonly used threshold techniques fail. We use maximum likelihood estimation algorithms to fit model distributions that account for the atom loss. This gives accurate atom number distributions for relatively few experimental runs (about 600 is sufficient) to sample a photon number distribution. We show that the method can be extended to situations when the photon number distributions for known initial atom numbers cannot be modeled, at the cost of requiring a higher number of experimental runs.
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